Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C2×#10596770⋊C2 |
| Fitting, socle | C25 ⋊ GO+(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10596770⋊C2 |
| commutator, cosocle | A4⋊S4 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C25 | GO+(4,𝔽2) |
| hypocenter | A42 | C2×D4 |
| LCS | G ▷ A4⋊S4 ▷ A42 | |
| UCS | C1 ◁ C2 | |
1064 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
40 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.